For the coconut cupcakes: Preheat oven to 350° F. Line a standard muffin tin with twelve paper liners. Set aside.

Add shredded coconut to the bowl of a food processor and pulse until finely ground. Transfer ground coconut to a medium bowl. To the bowl, flour, baking powder, and salt. Whisk to combine.

In the bowl of an electric stand mixer, cream butter and sugar on medium-high speed until pale and fluffy, about 3 minutes. Add egg, egg white, coconut extract, and vanilla extract, and beat until completely combined, occasionally scraping down the sides of the bowl. Reduce mixer speed to low and then add the coconut/flour mixture in three batches, alternating with two additions of coconut milk, and beating until each addition is just combined. Divide batter evenly between the lined cups.

Bake until a toothpick inserted in the center comes out just barely clean, about 18 minutes. Remove from oven and let cupcakes cool in the pan for 10 minutes, and then remove cupcakes to a wire rack to cool completely.

For the fluffy coconut buttercream: In the bowl of a stand mixer fitted with a paddle attachment, whip butter on medium-high speed until very fluffy, about 8 minutes, occasionally scraping down the sides and bottom of the bowl. Add powdered sugar and salt, and beat on low to incorporate. Add half and half, coconut extract, and vanilla extract, mixing on low until combined. Increase mixer speed to medium-high and beat until very light and fluffy, about 5 to 6 minutes, occasionally scraping down the sides and bottom of the bowl.

To assemble the cupcakes: Use a large cookie scoop (I use this one) to top each cupcake with a round of coconut buttercream. Gently tap the bottom of the cupcake on the counter once or twice to settle the buttercream onto the cupcake. The coconut buttercream recipe makes just enough frosting for twelve cupcakes frosted in this generous manner, so try not to snitch too much out of the bowl! Top the buttercream with some large flake coconut, if desired, to finish off the cupcakes.